Equações Diferenciais Simmons

The sole aim of science is the honor of the human mind,

and from this point of view

a question about numbers

is as important

as a question about the system of the world.

-C. G. J. Jacobi

DIFFERENTIAL

EQUATIONS

WITH APPLICATIONS AND

HISTORICAL NOTES

Second Edition

George F. Simmons

Professor of Mathematics

Colorado College

with a new chapter on numerical methods by

John S. Robertson

Department of Mathematical Sciences

United States Military Academy

McGraw-Hili, Inc.

New York S1. Louis San Francisco Auckland Bogota Caracas

Hamburg Lisbon London Madrid Mexico Milan Montreal

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This book was set in Times Roman.

The editors were Richard Wallis and John M. Morriss;

the production supervisor was Louise Karam.

The cover was designed by Carla Bauer.

Project supervision was done by The Universities Press.

R. R. Donnelley & Sons Company was printer and binder.

DIFFERENTIAL EQUATIONS WITH APPLICATIONS

AND HISTORICAL NOTES

Copyright @ 1991, 1972 by McGraw-Hill, Inc. All rights reserved. Printed in the United

States of America. Except as permitted under the United States Copyright Act of 1976,

no part of this publication may be reproduced or distributed in any form or by any

means, or stored in a data base or retrieval system, \\1:thout the prior written permission

of the publisher.

234567890 DOC DOC 954321

ISBN 0-07-057540-1

Library of Congress Cataloging-in- Publication Data

Simmons, George Finlay , (date).

Differential equations with applications and historical notes /

George F. Simmons.-2nd ed.

p. cm.

ISBN 0-07-057540-1

1. Differential equations. I. Title.

QA372.S49 1991

515' . 35--dc20

90-33686